king kyle

Can you provide another solution that also allows the equality to work? I cannot get the left side result to match the right side result when La differs from Lp.

I'm not sure what your getting at here. I would of thought that there would be a way to solve La in terms of Lp. If you look at this spreadsheet you will see that if La = Lp then the top equality holds.

But isn't La=Lp ?

La=Lp seems obvious to me too, I just don't how you would actually go about solving this.

I've stumbled upon a direct proof on Reddit, which uses differentiation to solve an equation. See https://medium.com/criminal-clouds/hydrostatic-lapse-part-1-of-3-e8a1534cd12d At particular point we reach this equation: This equation is then "logged" on both sides: then differentiated on both sides: then rearranged: then differentiated on both sides again and solved: Is this the correct way to solve this equation? I'm no maths expert, but this differentiation of both sides seems like far too much of a short cut.